Question

Find $x$: $\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+}}}...\infty =6$

Answer 1

Solve for $x$

Given, $\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+}}}...\infty =6$

We see that the first inner radical is the same as the outermost radical. Thus, the value of the inner radical is also $6$.

Substituting,

$\begin{array}{rrcl}\Rightarrow & \sqrt{x+6}& =& 6\\ \Rightarrow & x+6& =& 36\\ \Rightarrow & x& =& 30\end{array}$

Therefore, the value of $x$ is $30$.